Walter G. Chapman

SAFT: Equation-of-state solution model for associating fluids

An equation-of-state model has been developed for predicting phase equilibria, based on the Statistical Associating Fluid Theory (SAFT). The agreement with molecular simulation data has been found to be excellent at all the stages of model development; for associating spheres, mixtures of associating spheres, and non-associating chains. The model has been shown to reproduce experimental phase equilibrium data for a few selected real pure compounds.

Phase equilibria of associating fluids

As a continuation of our work on spherical associating molecules, we have derived expressions for changes in the thermodynamic properties due to association in mixtures of molecules with multiple bonding sites. The equations are written in terms of a hard-core reference whose pair distribution function is known. In practise, the hard-sphere reference mixture is the easiest to use. A reference system of homonuclear chains is examined in order to account for asymmetries in molecular shape; chains are constructed by bonding equal-sized spheres together. An equation of state for hard-sphere chains is obtained which is in good agreement with recent simulation data. Expressions for mixtures of homonuclear chains of different sizes are also presented. The approach is extended to examine associating chain molecules with multiple bonding sites. The phase equilibria of non-associating chains, and of associating chains with one or two bonding sites are determined. In this study, the separate effects of molecular ass...

Phase equilibria of associating fluids : spherical molecules with multiple bonding sites

The effect of molecular associations on the phase coexistence properties of fluids with one or two directional, attractive centres is investigated. The individual molecules are represented by hard-sphere repulsive cores with off-centre, square-well attractive sites. Such a system’s thermodynamic properties can be calculated by using expressions based on a theory recently proposed by Wertheim. Isothermal-isobaric Monte Carlo simulations of hard-sphere fluids with one or two attractive sites are shown to be in good agreement with the results of the theory. In order to study the system’s phase equilibria using the theory, a simple van der Waals mean-field term is added to account for the dispersion forces. The critical points and phase equilibria of the associating fluids are determined for various values of the strength and range of the attractive site. Furthermore, results are presented for the degree of association in the gas and liquid phases along the vapour pressure curve. The theory can treat fluids with strong hydrogen-bonding associations such as those found in the carboxylic acids, the aliphatic alcohols, hydrogen fluoride, water etc.

A NEW EQUATION OF STATE FOR HARD CHAIN MOLECULES

We present a new equation of state for hard chain fluids. This equation of state is developed by applying an extension of Wertheim’s theory for associating fluids to a nonspherical reference fluid. Since the equation of state is developed in a similar manner to the statistical associating fluid theory (SAFT) we call this improved equation of state SAFT‐Dimer (SAFT‐D). The equation of state requires only the contact values of the hard sphere and hard disphere site–site correlation functions as input. We compare the compressibility factor from SAFT and SAFT‐D with molecular simulation data for flexible hard chains with chain lengths of 16, 51, and 201 segments. The second virial coefficient and compressibility factor from SAFT‐D are in better agreement with molecular simulation results than the generalized Flory dimer, TPT2, and Percus–Yevick compressibility equations of state.

Modeling of Asphaltene Phase Behavior with the SAFT Equation of State

Abstract The SAFT equation of state was used to model asphaltene phase behavior in a model live oil and a recombined oil under reservoir conditions. The equation of state parameters for the asphaltenes were fit to precipitation data from oil titrations with n-alkanes at ambient conditions. The SAFT model was then used to predict the asphaltene stability boundaries in the live oils. A lumping scheme that divides the recombined oil into six pseudo-components based on composition, saturates–aromatics–resins–asphaltenes fractionation, and gas–oil-ratio data was introduced. Using this lumping scheme, SAFT predicted stock-tank oil and recombined oil densities that are in excellent agreement with experiment data. For both the model and the recombined oil systems, SAFT predicted asphaltene instability and bubble points agree well with experimental measurements.

Associating fluids with four bonding sites against a hard wall: density functional theory

We present two new perturbation density functional theories to investigate non-uniform fluids of associating molecules. Each fluid molecule is modelled as a spherical hard core with four highly anisotropic square well sites placed in tetrahedral symmetry on the hard core surface. In one theory we apply the weighting from Tarazonas hard sphere density functional theory to Wertheims bulk first-order perturbation theory. The other theory uses the inhomogeneous form of Wertheims theory as a perturbation to Tarazonas hard-sphere density functional theory. Each theory approaches Tarazonas theory in the limit of zero association. We compare results from theory and simulation for density profiles, fraction of monomers, and adsorption of an associating fluid against a hard, smooth wall over a range of temperatures and densities. The non-uniform fluid theory which uses Tarazonas weighting of Wertheims theory in the bulk is in good agreement with computer simulation results.

Microstructure of inhomogeneous polyatomic mixtures from a density functional formalism for atomic mixtures

A free energy density functional theory (DFT) for inhomogeneous polymeric mixtures is developed by treating the polyatomic system as a strongly associating atomic fluid mixture. The theory, derived in terms of segment density, retains the simple form of the DFTs for atomic fluids. Invoking the complete bonding limit of a stoichiometric mixture in the association free energy functional yields a computationally simple and accurate functional for the polyatomic system. Comparisons of theory calculations with molecular simulations are presented for inhomogeneous solutions and blends of linear and branched chains, demonstrating the capability of the theory to accurately capture the entropic and enthalpic effects governing the microstructure.

Application of Wertheim's thermodynamic perturbation theory to dipolar hard sphere chains

We present results from molecular simulation and statistical mechanics based theory for dipolar hard sphere chains. We consider tangent hard sphere chains with dipoles on alternate segments. The equation of state is obtained by applying Wertheims associating fluid theory in the total bonding limit to a mixture of non-polar and dipolar hard spheres. The equation of state of the chain requires the compressibility factor and pair correlation functions of this mixture which is the reference fluid. Computer simulation shows that the distribution function between the non-polar and polar hard spheres perpendicular to the dipole can be closely approximated by the hard sphere distribution function. This result is consistent with results from the mean spherical approximation and from reference linear hypernetted chain theory. With this approximation we propose an equation of state for dipolar hard sphere chains.

Theory and simulation for associating fluids with four bonding sites

In this paper we present new results from molecular simulation and theory for associating hard spheres and Lennard-Jones (LJ) spheres with four association or hydrogen-bonding sites. The association interaction is modelled with a highly anisotropic square well. Results from the first-order perturbation form of Wertheims theory are compared with simulation results. The agreement between simulation and theory for compressibility factor, configurational energy, fraction of monomers, and bonding distribution is good. We also obtained the cluster size distribution and the average cluster size from simulation. An expression based on the assumptions of the theory and statistical arguments was developed for the average cluster size. The agreement between simulation and this equation for average cluster size is good for small and moderate strengths of the association potential. Finally the vapour-liquid coexistence curves for associating LJ fluids were obtained from theory.

Modified interfacial statistical associating fluid theory: a perturbation density functional theory for inhomogeneous complex fluids.

A density functional theory based on Wertheims first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.